We trace the origin of the newly determined extragalactic gamma ray background from EGRET data to an unresolved population of blazars and neutralino annihilation in cold dark matter halos . Using results of high-resolution simulations of cosmic structure formation , we calculate composite spectra and compare with the EGRET data . The resulting best-fit value for the neutralino mass is \mathrm { m _ { \chi } = 515 _ { -75 } ^ { +110 } ~ { } GeV } ( systematic errors \mathrm { \sim 30 \% } ) .